What happened with theatre in the Middle Ages? Most overviews of theatre always mention Greek and Roman plays but then jump on to plays from Shakespeare or the Spanish Tragedy. Was it discontinued as a practice, do we have no records?

We know lots! There is an answer from last year by u/Dont_Do_Drama that should be helpful:

When I was in grad school, there was actually a group of actors associated with our department (but not really part of the school) that performed medieval plays, the Poculi Ludique Societas ("The Cup and Game Society")